The constitution derives it's authority from the Declaration of Independence. The Declaration of Independence derives it's authority from God.
Acts of Man do not override rights from God.
There is some truth in that. The Declaration can be viewed as one of our primary, founding documents. And, there are some who view the Mayflower Compact in the same way. "If it weren't for the Magna Carta, there would never have been a _______________."
However, it is the Constitution that provides the framework for our government and laws. Where there is a conflict between the Constitution and one of those other primary documents, it is the Constitution that prevails. There is, for example, tension between the assumptions underlying some of the provisions of the Declaration and the Thirteenth Amendment.
The Declaration of Independence derives it's authority from God.
There are people who believe that our Constitution is divinely inspired. So, what happens if there is a conflict? Answer: We follow the Constitution. And, if you suggest that there is no possible conflict, then you are merely suggesting that there will never be a need to consult the Declaration.
Acts of Man do not override rights from God.
How can anyone disagree with that? The obvious problem is that people often disagree about what God wants. You've studied our history leading up to the Civil War. What did you learn about how God feels about slavery? Didn't it depend on whom you asked?
Most people are reluctant to claim to speak for God when it comes to disagreements over earthly policies. However, if you look around the world, it isn't hard to find many people who believe that we as people have no right to disagree with what some religious leader believes at that time to be the word of God. In many places, these matters cannot even be safely debated - the interpretations of the religious leader have the force of law. Would you be willing to let Obama rule based upon his notions of God's will? Would you let him stone people if he claimed to find a Biblical provision to support it?
So, it all sounds good to talk about conforming our conduct to God's will. It's in the application that difficulties arise, even when it comes to simple things. How does God feel about parking meters? I am confident that there are people who can tell you if you ask them.
I prefer a system in which each person can develop his own personal relationship with God. I recognize that this preference leads to different interpretations of God's will. I recognize that some will conclude and have concluded that God prefers a system that allows for a bit of slavery, but I see things differently. However, I prefer to live with those differences than to turn all of our questions over to some figure of authority. We're all just people and we're all capable of error. There isn't anybody we can count on to be infallible or even "better than average" at divining God's will.